Publications

Books

• Carroll, Robert Wayne; Showalter, Ralph E. SINGULAR and DEGENERATE CAUCHY PROBLEMS.
  Mathematics in Science and Engineering, Vol. 127. Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1976. viii+333 pp.
  
  

• Showalter, R. E. HILBERT SPACE METHODS for PARTIAL DIFFERENTIAL EQUATIONS.
  Electronic reprint of the 1977 original. Electronic Monographs in Differential Equations, San Marcos, TX, 1994. iii+242 pp.,
  and it is now published by Dover.
  
  

• Showalter, R. E. MONOTONE OPERATORS in BANACH SPACE and NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS
  Mathematical Surveys and Monographs, 49. American Mathematical Society, Providence, RI, 1997. xiv+278 pp.
  
  

Papers

• Hosseinkhan, Alireza; Showalter, Ralph E., Semilinear Degenerate Biot-Signorini System,
  SIAM J. Mathematical Analysis 55 (2023), No. 5, pp.  5643--5665. [DOI: 10.1137/22M1505335]
  
  

• Peszyńska, M.; Showalter, Ralph E., Approximation of Hysteresis Functionals,
  Journal of Computational and Applied Mathemics 389 (2021) [DOI: 10.1016/j.cam.2020.113356]
  
  

• Hosseinkhan, Alireza; Showalter, Ralph E., Biot-Pressure System with Unilateral Displacement Constraints,
  Journal of Mathematical Analysis and Applications 497 (2021) Online.
  
  

• Peszyńska, M.; Showalter, Ralph E., Approximation of Scalar Conservation Law with Hysteresis,
  SIAM J. Numerical Analysis 58 (2020), No. 2, pp. 962--987. [DOI: 10.1137/18M1197679]
  
  

• Holland, Eleanor; Showalter, Ralph E., Poro-visco-elastic compaction in sedimentary basins,
  SIAM J. Mathematical Analysis 50 (2018), No. 2, pp. 2295--2316. [DOI: 10.1137/17M1141539]
  
  

• Morales, Fernando; Showalter, Ralph E., A Darcy-Brinkman model of fractures in porous media,
  Journal of Mathematical Analysis and Applications 452 (2017), pp. 1332-1358.
  
  

• Peszyńska, M.; Showalter, R. E.; Webster, Justin T., Advection of methane in the hydrate zone: model, analysis and examples,
  Mathematical Methods in the Applied Sciences 38 (2015) No. 18, pp. 4613-4629.
  
  

• Peszyńska, M.; Showalter, R. E.; Yi, Son-Young, Flow and transport when scales are not separated: numerical analysis and simulations of micro- and macro-models,
  Int. J. Numerical Analysis and Modeling 12 (2015) No. 3, pp. 476 - 515.
  
  

• Peszyńska, M.; Showalter, R. E.; Trykozko, A., Modeling, analysis, and simulation of processes in evolving porous media in applications to methane hydrate and biofilm modeling,
  Oberwolfach Workshop on Reactive Flows in Deformable, Complex Media, September 21-26, 2014, Eds. Margot Gerritsen, Jan Martin Nordbotten, Iuliu Sorin Pop, and Barbara Wohlmuth, Report No. 43/2014, p.19-20.
  
  

• Nguetseng, Gabriel; Showalter, Ralph E.; Woukeng, Jean Louis, Diffusion of a single-phase fluid through a general deterministic partially-fissured medium,
  Electronic J. Differential Equations 2014 (2014), No. 164, pp. 1-26 .
  
  

• Nathan L. Gibson, F. Patricia Medina, Malgorzata Peszynska, Ralph E. Showalter Evolution of phase transitions in methane hydrate,
  Journal of Mathematical Analysis and Applications 409 (2014), pp. 816-833.
  
  

• Morales, Fernando; Showalter, Ralph E. Interface approximation of Darcy flow in a narrow channel,
  Mathematical Methods in the Applied Sciences 35 (2012), pp. 182-195.
  
  

• Muntean, A.; Ptashnyk, M.; Showalter, R. E. (editors), Analysis and Approximation of Microstructure Models,
  Preface to Special Issue, Applicable Analysis, Vol. 91 (2012), No. 6, 1053-1054.
  
  

• Yi, Son-Young; Peszyńska, M.; Showalter, R. E. Numerical upscaled model of transport with non-separated scales,
  Proceedings of XVIII Conference on Computational Methods in Water Resources, (Barcelona, 2010), J. Carrera (ed.), #188.
  
  

• Showalter, R. E. Nonlinear degenerate evolution equations in mixed formulation,
  SIAM J. Math. Anal. 42 (2010), No. 5, pp. 2114--2131. [DOI: 10.1137/100789427]
  
  

• Morales, Fernando; Showalter, Ralph E. The narrow fracture approximation by channeled flow,
  Journal of Mathematical Analysis and Applications 365 (2010), pp. 320-331.
  
  

• Peszyńska, M.; Showalter, R. E.; Yi, Son-Young Homogenization of a pseudo-parabolic system,
  Applicable Analysis 88 (2009), No. 9, pp. 1265--1282.
  
  

• Peszyńska, M.; Showalter, R. E.; Spagnuolo, A.; Walkington, N. (editors), Modeling, Analysis and Simulation of Multiscale Nonlinear Systems,
  Preface to Special Issue, International Journal of Numerical Analysis and Modeling, Vol. 5 (2008), Supp.
  
  

• Peter, Malte; Showalter, Ralph E. Homogenization of Secondary-Flux Models of Partially Fissured Media ,
  Int. J. Numerical Analysis and Modeling 5 Supp. (2008), pp. 150-156.
  
  

• Peszyńska, M.; Showalter, R. E. Multiscale Elliptic-Parabolic Systems for Flow and Transport ,
  Electronic J. Differential Equations 2007 (2007), No. 147, pp. 1-30.
  
  

• Showalter, R. E. Poro-Plastic Filtration Coupled to Stokes Flow,
  Abousleiman, Y., Cheng, A.H.-D., and Ulm, F.-J. (eds.), Poromechanics III-Biot Centennial (1905-2005),
  Proceedings, 3rd Biot Conference on Poromechanics, A.A. Balkema, Leidon/London/New York/Philadelphia/Singapore, pp. 523-528, 2005.
  ICES Report 04-56.
  
  

• V. S. Manoranjan; R. Showalter; Hong-Ming Yin On Two-Phase Stefan Problem Arising from a Microwave Heating Process,
  Discrete and Continuous Dynamical Systems [Series A: Mathematical Analysis] 15 (2006), 1155 - 1168.
  WSU Technical Report 2004-8.
  
  

• Showalter, R. E. Poroelastic Filtration Coupled to Stokes Flow,
  Lecture Notes in Pure and Applied Mathematics, vol. 242, "Control Theory of Partial Differential Equations", (Georgetown University, May, 2003), O. Imanuvilov, G. Leugering, Roberto Triggiani, and Bing-Yu Zhang (editors), pp. 229 - 241, Chapman & Hall, Boca Raton, 2005.
  ICES Report 04-28.
  
  

• Showalter, R. E.; Ulisse Stefanelli Diffusion in Poro-Plastic Media,
  Mathematical Methods in the Applied Sciences 27 (2004), 2131--2151.
  TICAM Report 03-22.
  
  

• Showalter, R. E. Diffusion in Deforming Porous Media,
  Dynamics of Continuous, Discrete and Impulsive Systems [Series A: Mathematical Analysis] 10 (2003), 661--678.
  TICAM Report 02-37.
  
  

• Visarraga, Darrin; Showalter, R. E. Double-Diffusion Models from a Highly-Heterogeneous Medium,
  Journal of Mathematical Analysis and Applications 295 (2004), 191-210.
  TICAM Report 02-23.
  
  

• Showalter, R. E.; Ning Su Partially Saturated Flow in a Composite Poroelastic Medium,
  Poromechanics II, (Grenoble, 2002), J.-L. Auriault et al (editors), pp.549--554, Balkema, Lisse, 2002.
  TICAM Report 02-15.
  
  

• Visarraga, Darrin; Showalter, R. E. Absorption-Delay Models of Heat Transport,
  Mathematical Models and Methods in Applied Sciences 13 (2003), 645-660.
  TICAM Report 02-01.
  
  

• Su, Ning; Showalter, R. E. Partially Saturated Flow in a Poroelastic Medium,
  Discrete Contin. Dynam. Systems [Series B: Applications & Algorithms] 1 (2001), 403-420.
  TICAM Report 01-01.
  
  

• Momken, Bahareh; Showalter, R. E. Single-phase Flow in Composite Poro-elastic Media,
  Mathematical Methods in the Applied Sciences 25 (2002), 115-139.
  TICAM Report 00-31.
  
  

• Pak, Hee-Chul; Showalter, R. E. Thin-Film Capacitance Models,
  Applicable Analysis 78 (2001), 415-451.
  TICAM Report 00-19.
  
  

• Showalter, R. E. Diffusion in Deformable Media,
  IMA Volumes in Mathematics and its Applications, vol. 131, "Resource Recovery, Confinement, and Remediation of Environmental Hazards", (Minneapolis, February, 2000), J. Chadam, A. Cunningham, R. Ewing, P. Ortoleva, and M. Wheeler (editors), pp. 115--130, Springer, New York.
  TICAM Report 00-18.
  
  

• K.-H. Hoffmann; Showalter, R. E. Vibration of a Shape Memory Alloy Wire,
  Communications in Applied Analysis 7 (2003), 53-66.
  TICAM Report 00-09.
  
  

• Showalter, R. E. Diffusion in Poro-Elastic Media,
  Journal of Mathematical Analysis and Applications 251 (2000), 310-340.
  TICAM Report 00-05.
  
  

• Clark, G. W.; Showalter, R. E. Two-Scale convergence of a Model for Flow in a Partially Fissured Medium,
  Electronic J. Differential Equations 1999, No. 2, 20 pp. (electronic). 76S05 (35Q35 73B27)
  
  

• Peszyńska, M.; Showalter, R. E. A Transport Model with Adsorption Hysteresis,
  Differential and Integral Equations 11 (1998), 327-340.
  
  

• Showalter, R. E.; Shi, Peter Dynamic Plasticity Models,
  Symposium on Advances in Computational Mechanics, Vol. 4 (Austin, TX, 1997).
  Comput. Methods Appl. Mech. Engrg. 151 (1998), no. 3-4, 501--511. (Reviewer: Martin Brokate) 73Exx
  
  

• Lectures on Flow in Porous Media,
  III Coloquio sobre Ecuaciones Diferenciales y Aplicaciones, Maracaibo, Venezuela,
  Angel Domingo Rueda and Jorge Gui\~nez (editors), Universidad del Zulia, 1998, pp. 53--97.
  
  

• Showalter, Ralph E. Micro-Structure Models of Porous Media,
  in HOMOGENIZATION and POROUS MEDIA, 183--202, 259--275,
  Interdiscip. Appl. Math., 6, Springer, New York, 1997. 76S05
  
  

• Douglas, J., Jr.; Peszyńska, M.; Showalter, R. E. Single Phase Flow in Partially Fissured Media,
  Transport in Porous Media 28 (1997), 285--306.
  
  

• Showalter, R. E.; Shi, Peter Plasticity models and nonlinear semigroups.
  Journal of Mathematical Analysis and Applications 216 (1997), no. 1, 218--245. (Reviewer: Martin Brokate) 73Exx (35Q72 47H20)
  
  

• Showalter, Ralph E.; Little, Thomas D.; Hornung, Ulrich Parabolic PDE with Hysteresis,
  Distributed parameter systems: modelling and control (Warsaw, 1995).
  Control Cybernet. 25 (1996), no. 3, 631--643. (Reviewer: Pavel Krej\v c�) 35K85 (35K65 47H30 47N20)
  
  

• Packer, L. A.; Showalter, R. E. The regularized layered medium equation.
  Applicable Analysis 58 (1995), no. 1-2, 137--155. 35Q35 (34G10 47H15)
  
  

• Packer, Lindsay; Showalter, Ralph E. Distributed capacitance microstructure in conductors.
  Appliable Analysis 54 (1994), no. 3-4, 211--224. 35Q60 (47N20 78A55)
  
  

• Little, T. D.; Showalter, R. E. The super-Stefan problem.
  Internat. J. Engrg. Sci. 33 (1995), no. 1, 67--75. 80A22 (35K05 35R35)
  
  

• Cook, John D.; Showalter, R. E. Microstructure diffusion models with secondary flux.
  Journal of Mathematical Analysis and Applications 189 (1995), no. 3, 731--756. 76R50 (35Q35 76S05)
  
  

• Hollingsworth, Brooke L.; Showalter, R. E. Semilinear degenerate parabolic systems and distributed capacitance models.
  Discrete Contin. Dynam. Systems 1 (1995), no. 1, 59--76. (Reviewer: Pierre A. Vuillermot) 35K65 (34G20 35K55 35Q35)
  
  

• Clark, G. W.; Showalter, R. E. Fluid flow in a layered medium.
  Quart. Appl. Math. 52 (1994), no. 4, 777--795. (Reviewer: Jean-Luc Guermond) 76S05 (35Q35 73B27)
  
  

• Hornung, Ulrich; Showalter, R. E. Elliptic-parabolic equations with hysteresis boundary conditions.
  SIAM J. Math. Anal. 26 (1995), no. 4, 775--790. (Reviewer: Nobuyuki Kenmochi) 35M10 (35K65 35R70 47H30 47N20)
  
  

• Rulla, J.; Showalter, R. E. Diffusion in partially fissured media and implicit evolution systems.
  Adv. Math. Sci. Appl. 5 (1995), no. 1, 163--191. (Reviewer: Georgii A. Sviridyuk) 34G20 (35K70 47N20 76R50)
  
  

• Little, T. D.; Showalter, R. E. Semilinear parabolic equations with Preisach hysteresis.
  Differential Integral Equations 7 (1994), no. 3-4, 1021--1040. (Reviewer: Maurice Gaultier) 35K55 (35R15 47H06 47H30 47N20)
  
  

• Showalter, Ralph E. Distributed microstructure models of porous media.
  Flow in porous media (Oberwolfach, 1992), 155--163, Internat. Ser. Numer. Math., 114, Birkh�user, Basel, 1993. 76S05 (35B27 35K99 73B27)
  
  

• Cook, John D.; Showalter, R. E. Distributed systems of PDE in Hilbert space.
  Differential Integral Equations 6 (1993), no. 5, 981--994. (Reviewer: Mei Ke Zhou) 35R20 (34G20 35K22 35Q35 47H20 47N20)
  
  

• Hornung, Ulrich; Showalter, R. E. PDE-Models with Hysteresis on the Boundary,
  in Models of hysteresis (Trento, 1991), 30--38,
  Pitman Res. Notes Math. Ser., 286, Longman Sci. Tech., Harlow, 1993. (Reviewer: J. R. Ockendon) 35K20 (47H30 47N20 76S05 93C10)
  
  

• Showalter, R. E.; Walkington, N. J. Elliptic systems for a medium with microstructure.
  Geometric analysis and nonlinear partial differential equations (Denton, TX, 1990), 91--104,
  Lecture Notes in Pure and Appl. Math., 144, Dekker, New York, 1993. (Reviewer: Wolfgang R�prich) 35J50 (35B30 35J70 73B05 73V25)
  
  

• Showalter, R. E.; Walkington, N. J. Diffusion of fluid in a fissured medium with microstructure.
  SIAM J. Math. Anal. 22 (1991), no. 6, 1702--1722. (Reviewer: L. Hsiao) 35K50 (35K65 76R50 76S05)
  
  

• Showalter, R. E.; Walkington, N. J. A hyperbolic Stefan problem.
  Current directions in nonlinear partial differential equations (Provo, UT, 1987).
  Rocky Mountain J. Math. 21 (1991), no. 2, 787--797. (Reviewer: P. D. Panagiotopoulos) 35R35 (35L10 49J20 80A22)
  
  

• Showalter, R. E.; Walkington, N. J. Micro-structure models of diffusion in fissured media.
  Journal of Mathematical Analysis and Applications 155 (1991), no. 1, 1--20. (Reviewer: Paul G. Schmidt) 35Q35 (35A15 76R50 76S05)
  
  

• Hornung, Ulrich; Showalter, Ralph E. Diffusion models for fractured media.
  Journal of Mathematical Analysis and Applications 147 (1990), no. 1, 69--80. (Reviewer: Yanis C. Yortsos) 76R50 (73B27 76S05)
  
  

• Showalter, Ralph E.; Walkington, Noel J. A diffusion system for fluid in fractured media.
  Differential Integral Equations 3 (1990), no. 2, 219--236. (Reviewer: Peter Knabner) 35K65 (35K60 35R35 76R50 76S05 76T05)
  
  

• Showalter, R. E.; Xu, Xiangsheng An approximate scalar conservation law from dynamics of gas absorption.
  J. Differential Equations 83 (1990), no. 1, 145--165. 35L65 (47H15 76S05)
  
  

• Showalter, R. E. Diffusion in a fissured medium with micro-structure.
  Free boundary problems in fluid flow with applications (Montreal, PQ, 1990), 136--141,
  Pitman Res. Notes Math. Ser., 282, Longman Sci. Tech., Harlow, 1993. 76S05 (76R50)
  
  

• Showalter, R. E.; Walkington, N. J. A hyperbolic Stefan problem.
  Free boundary problems: theory and applications, Vol. II (Irsee, 1987), 840--844,
  Pitman Res. Notes Math. Ser., 186, Longman Sci. Tech., Harlow, 1990. 35R35 (34G20 35L20)
  
  

• Bosse, Marie-Pascale; Showalter, R. E. Homogenization of the layered medium equation.
  Applicable Analysis 32 (1989), no. 3-4, 183--202. (Reviewer: Lumin Jiang) 35K99 (35B25 35B40 94C05)
  
  

• Carey, G. F.; Jiang, B.-N.; Showalter, R. A regularization-stabilization technique for nonlinear conservation equations.
  Int. Jour. Numer. Methods Partial Differential Equations 4 (1988), no. 3, 165--171. 65M60
  
  

• Showalter, R. E.; Xu, Xiangsheng Convergence of diffusion with concentrating capacity.
  Journal of Mathematical Analysis and Applications 137 (1989), no. 1, 132--147. (Reviewer: D. Hinton) 78A30 (35B25)
  
  

• Showalter, R. E. Implicit evolution equations.
  Differential equations and applications, Vol. I, II (Columbus, OH, 1988), 404--411, Ohio Univ. Press, Athens, OH, 1989. 35K99 (76Rxx 76S05)
  
  

• Showalter, R. E.; Walkington, N. J. A hyperbolic Stefan problem.
  Quart. Appl. Math. 45 (1987), no. 4, 769--781. (Reviewer: Vasilios Alexiades) 35R35 (35L99 80A20)
  
  

• Rulla, Jim; Showalter, R. E. Diffusion with prescribed convection in fissured media.
  Differential Integral Equations 1 (1988), no. 3, 315--325. (Reviewer: Li Shang Jiang) 35R35 (35K50 80A20)
  
  

• Showalter, R. E. The fissured medium equation.
  Physical mathematics and nonlinear partial differential equations (Morgantown, W. Va., 1983), 199--205,
  Lecture Notes in Pure and Appl. Math., 102, Dekker, New York, 1985. (Reviewer: M. Shearer) 76S05 (35Q20)
  
  

• Böhm, Michael; Showalter, R. E. A nonlinear pseudoparabolic diffusion equation.
  SIAM J. Math. Anal. 16 (1985), no. 5, 980--999. (Reviewer: Jean Genet) 35K55
  
  

• Showalter, R. E. Cauchy problem for hyperparabolic partial differential equations.
  Trends in the theory and practice of nonlinear analysis (Arlington, Tex., 1984), 421--425,
  North-Holland Math. Stud., 110, North-Holland, Amsterdam-New York, 1985. (Reviewer: J. A. Donaldson) 35K15 (35D05)
  
  

• Showalter, R. E. VARIATIONAL THEORY and APPROXIMATION of BOUNDARY VALUE PROBLEMS.
  Numerical analysis, Lancaster 1984 (Lancaster, 1984), 140--179,
  Lecture Notes in Math., 1129, Springer, Berlin-New York, 1985. (Reviewer: William W. Hager) 65N30
  
  

• Böhm, Michael; Showalter, R. E. Diffusion in fissured media.
  SIAM J. Math. Anal. 16 (1985), no. 3, 500--509. (Reviewer: Vasile M. Ionescu) 76S05 (35Q20 76A02)
  
  

• Showalter, Ralph E. A singular quasilinear diffusion equation in $L\sp{1}$.
  J. Math. Soc. Japan 36 (1984), no. 2, 177--189. (Reviewer: Jurgen Appell) 35K60 (34G20)
  
  

• Showalter, R. E. Local regularity, boundary values and maximum principles for pseudoparabolic equations.
  Applicable Analysis 16 (1983), no. 3, 235--241. 35K70 (35B50)
  
  

• Showalter, R. E. Two Stefan problems for a degenerate parabolic system.
  Dynamical systems, II (Gainesville, Fla., 1981), 367--374, Academic Press, New York-London, 1982. (Reviewer: William Rundell) 35K65 (35R35 80A20)
  
  

• DiBenedetto, Emmanuele; Showalter, R. E. A free-boundary problem for a degenerate parabolic system.
  J. Differential Equations 50 (1983), no. 1, 1--19. (Reviewer: Mario Primicerio) 35R35 (35K65 76S05 80A20)
  
  

• Showalter, R. E. Degenerate nonlinear parabolic systems and free-boundary problems.
  Applied nonlinear functional analysis (Berlin, 1981), pp. 289--300, Methoden Verfahren Math. Phys., 25, Lang, Frankfurt, 1983. 35K65 (35R35 80A15)
  
  

• Showalter, R. E. Mathematical formulation of the Stefan problem.
  Internat. J. Engrg. Sci. 20 (1982), no. 8, 909--912. (Reviewer: Emmanuele di Benedetto) 80A20 (35R35)
  
  

• DiBenedetto, Emmanuele; Showalter, R. E. A pseudoparabolic variational inequality and Stefan problem.
  Nonlinear Anal. 6 (1982), no. 3, 279--291. (Reviewer: William Rundell) 35K85 (47H05 49A29)
  
  

• DiBenedetto, Emmanuele; Showalter, R. E. Implicit degenerate evolution equations and applications.
  SIAM J. Math. Anal. 12 (1981), no. 5, 731--751. (Reviewer: Gregory B. Passty) 47H15 (34G20 35K65)
  
  

• Showalter, R. E. Singular nonlinear evolution equations.
  Rocky Mountain J. Math. 10 (1980), no. 3, 499--507. (Reviewer: A. Pazy) 34G20 (34A60 47H05 49A50)
  
  

• Showalter, R. E. Perturbation of maximal accretive operators with right angle.
  Portugal. Math. 36 (1977), no. 2, 79--82 (1980). (Reviewer: K. K. Oberai) 47B44
  
  

• Showalter, R. E. Initial and final value problems for degenerate parabolic evolution systems.
  Indiana Univ. Math. J. 28 (1979), no. 6, 883--893. (Reviewer: J. E. Lagnese) 34G10 (35K22)
  
  

• Showalter, R. E. Degenerate parabolic initial-boundary value problems.
  J. Differential Equations 31 (1979), no. 3, 296--312. (Reviewer: Curtis C. Travis) 35G30 (34G10 35K65)
  
  

• Showalter, R. E. A Green's formula for weak solutions of variational problems.
  Applied nonlinear analysis (Proc. Third Internat. Conf., Univ. Texas, Arlington, Tex., 1978), pp. 381--387, Academic Press, New York-London, 1979. (Reviewer: Alfonso Castro) 49A22 (35A15 49A29)
  
  

• Showalter, R. E. Sobolev equations for nonlinear dispersive systems.
  Applicable Analysis 7 (1977/78), no. 4, 297--308. (Reviewer: W. G�ttinger) 34G20 (35Q20)
  
  

• Goldstein, Jerome A.; Radin, Charles; Showalter, R. E. Convergence rates of ergodic limits for semigroups and cosine functions.
  Semigroup Forum 16 (1978), no. 1, 89--95. (Reviewer: G. F. Webb) 47D05 (47A35)
  
  

• Showalter, R. E. Quasi-reversibility of first and second order parabolic evolution equations.
  Improperly posed boundary value problems (Conf., Univ. New Mexico, Albuquerque, N.M., 1974), pp. 76--84.
  Res. Notes in Math., No. 1, Pitman, London, 1975. 34G05 (35K99 47D05)
  
  

• Showalter, R. E. Well-posed problems for some nonlinear dispersive waves.
  J. Math. Pures Appl. (9) 56 (1977), no. 2, 123--135. (Reviewer: Alan Jeffrey) 35Q99 (76.35)
  
  

• Showalter, R. E. Regularization and approximation of second order evolution equations.
  SIAM J. Math. Anal. 7 (1976), no. 4, 461--472. (Reviewer: M. Artola) 34G05 (35R20)
  
  

• Showalter, R. E. The Sobolev equation. II.
  Applicable Analysis 5 (1975), no. 2, 81--99. (Reviewer: Tapas Mazumdar) 35R20
  
  

• Showalter, R. E. The Sobolev equation. I.
  Applicable Analysis 5 (1975), no. 1, 15--22. (Reviewer: Tapas Mazumdar) 35R20
  
  

• Showalter, R. E. Nonlinear degenerate evolution equations and partial differential equations of mixed type.
  SIAM J. Math. Anal. 6 (1975), 25--42. (Reviewer: J. A. Goldstein) 47H15 (35R20)
  
  

• Showalter, R. E. A priori error estimates for approximation of parabolic boundary value problems.
  SIAM J. Numer. Anal. 12 (1975), 456--463. (Reviewer: G. W. Hedstrom) 65N15
  
  

• Showalter, R. E. A nonlinear parabolic-Sobolev equation.
  Journal of Mathematical Analysis and Applications 50 (1975), 183--190. (Reviewer: J. E. Lagnese) 35Q99 (47H15)
  
  

• Showalter, R. E. The final value problem for evolution equations.
  Journal of Mathematical Analysis and Applications 47 (1974), 563--572. (Reviewer: H. O. Fattorini) 34G05 (47D05)
  
  

• Showalter, R. E. Continuity of maximal monotone sets in Banach space.
  Proc. Amer. Math. Soc. 42 (1974), 543--546. (Reviewer: R. Kannan) 47H05
  
  

• Showalter, R. E. Degenerate evolution equations and applications.
  Indiana Univ. Math. J. 23 (1974), 655--677. (Reviewer: J. E. Lagnese) 47F05 (35R20)
  
  

• Showalter, R. E. Equations with operators forming a right angle.
  Pacific J. Math. 45 (1973), 357--362. (Reviewer: J. E. Lagnese) 47D05 (47B44)
  
  

• Showalter, R. E.; Ting, T. W. Asymptotic behavior of solutions of pseudo-parabolic partial differential equations.
  Ann. Mat. Pura Appl. (4) 90 (1971), 241--258. (Reviewer: Howard A. Levine) 35B40
  
  

• Showalter, R. E. Existence and representation theorems for a semilinear Sobolev equation in Banach space.
  SIAM J. Math. Anal. 3 (1972), 527--543. (Reviewer: G. Ladas) 34G05 (47H15)
  
  

• Showalter, R. E. Weak solutions of nonlinear evolution equations of Sobolev-Galpern type.
  J. Differential Equations 11 (1972), 252--265. (Reviewer: J. E. Lagnese) 35R20 (47H15)
  
  

• Showalter, R. E. Local regularity of solutions of Sobolev-Galpern partial differential equations.
  Pacific J. Math. 34 1970 781--787. (Reviewer: N. Shimakura) 35.24
  
  

• Showalter, R. E. Well-posed problems for a partial differential equation of order $2m+1$.
  SIAM J. Math. Anal. 1 1970 214--231. (Reviewer: J. E. Lagnese) 35.65
  
  

• Showalter, R. E. Partial differential equations of Sobolev-Galpern type.
  Pacific J. Math. 31 1969 787--793. (Reviewer: J. E. Lagnese) 35.79
  
  

• Showalter, R. E.; Ting, T. W. Pseudoparabolic partial differential equations.
  SIAM J. Math. Anal. 1 (1970), 1--26. 35K99
  
  

• Advances in differential and integral equations. A collection of papers presented at the Conference on Qualitative Theory of Nonlinear Differential and Integral Equations held at the University of Wisconsin, Madison, Wis., August 12--23, 1968. In memoriam: Rudolph E. Langer (March 8, 1894 to March 11, 1968). Edited by John A. Nohel. Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1969.